Abstract

Some idealized three-dimensional objects approaching a fixed observation point along a symmetrical radial track yield invariant, but paradoxical, optical geometrical effects. Texture elements on a sphere are progressively self-occluded by the visible boundary of the sphere, until, at contact with the observation point, only a single element (point) is available; paradoxically, that single point comes to fill the entire frontal optical field. Optical velocity of a texture element on an approaching spinning sphere goes to infinity, whereas paradoxically the surface area visible goes to zero. Texture elements on the surface of a circular cone approaching an observation point apex-first disappear at contact with the observation point, whereas paradoxically the optical angle subtended by the cone expands to a maximum. With planar objects, off-track texture elements disappear, whereas paradoxically a single central element fills the frontal optical field. Rationalizing the complementary nature of such changing patterns suggests the utility of the global array hypothesis. Extensions to optical information for modeled surfaces are discussed, with a call for additional study of the geometry of optical approach.

摘要

一些理想的三维物体沿着对称的径向轨迹接近固定的观察点会产生不变但反常的光学几何效果。球体上的纹理元素逐渐被球体的可见边界自我遮挡，直到与观察点接触时，只有一个元素（点）可用；矛盾的是，这个单点充满了整个额叶光学场。临近旋转的球体上纹理元素的光速达到无穷大，而自相矛盾的是可见的表面积为零。接近观察点的圆锥体表面上的纹理元素在与观察点接触时先消失，而自相矛盾的是，圆锥体所具有的光学角度最大。对于平面物体，偏离轨道的纹理元素消失了，而自相矛盾的是，一个中央元素填充了正面的光场。合理化这种变化模式的互补性质表明了全局阵列假说的实用性。讨论了对建模表面的光学信息的扩展，并呼吁对光学方法的几何形状进行其他研究。